A168601 E.g.f. A(x) satisfies A(x) = exp( x*A(2*x)^3 ).

1, 1, 13, 577, 65737, 17553361, 10704000277, 14796719274961, 46078793355045073, 320622833897384770657, 4940987529761176087132381, 167239138427197351352909547169, 12340269209872740741602975099855641

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

a(0) = 1; a(n) = 2^(n-1) * (n-1)! * Sum_{i, j, k, l>=0 and i+j+k+l=n-1} (n-i)/2^i * a(i) * a(j) * a(k) * a(l)/(i! * j! * k! * l!). - Seiichi Manyama, Jul 06 2025

Example

E.g.f: A(x) = 1 + x + 13*x^2/2! + 577*x^3/3! + 65737*x^4/4! +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=exp(x*subst(A, x, 2*x)^3) ); n!*polcoeff(A, n)}

Crossrefs

Cf. A096538, A168600.

Cf. A360988.

Sequence in context: A050286 A096761 A076461 * A142210 A109875 A258303

Adjacent sequences: A168598 A168599 A168600 * A168602 A168603 A168604

Keyword

nonn

Author

Paul D. Hanna, Dec 05 2009

Status

approved